Horizons as boundary conditions in spherical symmetry

Abstract

We initiate the development of a horizon-based initial (or rather final) value formalism to describe the geometry and physics of the near-horizon spacetime: data specified on the horizon and a future ingoing null boundary determine the near-horizon geometry. In this initial paper we restrict our attention to spherically symmetric spacetimes made dynamic by matter fields. We illustrate the formalism by considering a black hole interacting with a) inward-falling, null matter (with no outward flux) and b) a massless scalar field. The inward-falling case can be exactly solved from horizon data. For the more involved case of the scalar field we analytically investigate the near slowly evolving horizon regime and propose a numerical integration for the general case.

Horizons in a binary black hole merger I: Geometry and area increase

“…Local constructions of spacetime neighborhoods near non-expanding horizons is given in [55,63,[66][67][68][69][70][71]. All stationary black holes and Killing horizons, including of course the Schwarzschild and Kerr black holes, are non-expanding horizons.…”

Evolving black hole with scalar field accretion

“…for exact non-static black hole solutions sourced by a null fluid 2. A purely ingoing flux at the apparent horizon T ab n a n b = 0 has been considered earlier as a boundary condition for a null fluid with traceless stress-energy tensor in Ref [15].…”